A diagnostic analysis of the climatological annual mean and seasonal cycle of
the Angola–Benguela Frontal Zone (ABFZ) is performed by applying an ocean
frontogenetic function (OFGF) to the
ocean mixing layer (OML). The OFGF reveals that the meridional confluence and
vertical tilting terms are the most dominant contributors to the
frontogenesis of the ABFZ. The ABFZ shows a well-pronounced semiannual cycle
with two maximum (minimum) peaks in April–May and November–December
(February–March and July–August). The development of the two maxima of
frontogenesis is due to two different physical processes: enhanced tilting
from March to April and meridional confluence from September to October. The
strong meridional confluence in September to October is closely related to
the seasonal southward intrusion of tropical warm water to the ABFZ that
seems to be associated with the development of the Angola Dome northwest of
the ABFZ. The strong tilting effect from March to April is attributed to the
meridional gradient of vertical velocities, whose effect is amplified in this
period due to increasing stratification and shallow OML depth. The proposed
OFGF can be viewed as a tool to diagnose the performance of coupled general
circulation models (CGCMs) that generally fail at realistically simulating
the position of the ABFZ, which leading to huge warm biases in the
southeastern Atlantic.

The ABFZ region also poses one of the major challenges for the global climate modeling
community. Most CGCMs exhibit a huge warm SST bias in the ABFZ (e.g., Zuidema et al.,
2016) and fail to reproduce the realistic SST,
its seasonal cycle, and the right location of the ABFZ (e.g., Koseki et al., 2017). While
Colberg and Reason (2006) and Giordani and Caniaux (2011) concluded that the position of the ABFZ is controlled, to a large extent, by the
local wind stress curl, Koseki et al. (2018) elucidated that the local wind stress curl
bias in CGCMs contributes partly to the warm SST bias in the ABFZ via erroneous intrusion
of tropical warm water, which is induced by a negative wind stress curl and enhanced
Angola Current. In order to comprehensively understand the sources of such model biases,
one needs to understand the processes of generation of the ABFZ.

Previous studies have mainly focused on the SST variability at interannual to decadal
timescales in the ABFZ, and/or on its impacts on regional climate that are well-studied
(e.g., Rouault et al., 2003; Lutz et al., 2015; Vizy et al., 2018). Whereas Morholz et
al. (1999) analyzed the ABFZ during a particular event in 1999, to our knowledge there
are few or no works quantitatively investigating dynamical and thermodynamical processes
responsible for the climatological state of the ABFZ and its seasonal cycle. A dynamical
diagnosis for the SST front in the north of the Atlantic cold tongue (e.g., Hasternrath
and Lamb, 1978; Giordani et al., 2013) was proposed by Giordani and Caniaux (2014,
hereafter referred to as GC2014). The frontogenetic function they use is, in general,
adapted to explore sources of frontogenesis of atmospheric synoptic-scale cyclones in the
extratropics (e.g., Keyser et al., 1988; Giordani and Caniaux, 2001). Using a
frontogenetic function, GC2014 clearly showed that the convergence associated with the
northern South Equatorial Current and Guinea Current forces the SST-front intensity
(frontogenetic effect), whereas mixed-layer turbulent flux destroys the SST front
(frontolytic effect). Fundamentally, the frontogenetic function consists of three
mechanical terms (confluence, shear, and tilting) and two thermodynamical terms (diabatic
heating and vertical mixing). Around the ABFZ, all these terms can be considered to be
contributors to the frontogenesis due to (1) the confluence zone associated with the
southward Angola and northward Benguela currents (confluence and shear), (2) strong
coastal upwelling (tilting) associated with the Benguela Current, (3) spatial variations
in radiative fluxes induced by the stratocumulus cloud deck (diabatic heating related to
radiation) associated with the cold SST and subsidence due to the St. Helena anticyclone
(e.g., Klein and Hartmann, 1993; Pfeifroth et al., 2012). So far, the relative roles of
these different processes in the frontogenesis of the ABFZ still need to be investigated.

In this study, following the fundamental philosophy of GC2014, we attempt to
understand the mechanisms responsible for the climatological ABFZ development
at a seasonal timescale based on a first-order estimation. We propose an
ocean frontogenetic function (OFGF) in a different way from GC2014 focusing on the OML mean front. The
structure of the remainder of this paper is as follows. Sect. 2 gives details
of dataset used in this study. In Sect. 3, we derive the OFGF. Section 4
provides a description of the climatological state around the ABFZ. In
Sect. 5, we apply our diagnostic methodology to the ABFZ and determine the
main terms of the frontogenetic function controlling its annual mean and
seasonal cycle. The associated processes are discussed in Sect. 6. Finally we
summarize and make some concluding remarks in Sect. 7.

For an overview of SST and its meridional gradient in the ABFZ, and
evaluation of the reanalysis data, we employ the optimum interpolated sea
surface temperature (OISST; Reynolds et al., 2007) released by the National
Oceanic and Atmospheric Administration (NOAA) that has 0.25∘of
horizontal resolution and daily temporal resolution from 1982 to 2010. For
the 3-D diagnostic analysis of the ABFZ, we utilize 1 h forecast data of the
Climate Forecast System Reanalysis (CFSR; Saha et al., 2010) developed by the
National Centers for Environmental Prediction (NCEP). The ocean component of
this system is based on Modular Ocean Model (MOM) version 4p0d (Griffies et
al., 2004) and implements data assimilation for the forecast. This system
provides 6-hourly data with a 0.5∘ horizontal resolution and
70 vertical layers for ocean. This resolution is relatively coarse compared
to the resolution of simulations performed with regional ocean models in a
forced mode using wind forcing from satellite products. However, the
advantage of a coupled ocean–atmosphere system like CFSR is that it allows
for avoiding spurious effects in wind forcing over coastal regions resulting
from the extrapolation in a 25–50 km width coastal fringe where the wind
cannot be observed by scatterometers (Astudillo et al., 2017). Moreover, the
wind satellite products are generally available for only a relatively short
time period, limiting investigation of long-term climatology and seasonal
cycle. In this paper we will analyze daily means (the procedure of data
post-processing is given in the Supplement) and utilize the CFSR outputs of
velocity (horizontal and vertical), potential temperature, net surface heat
flux, OML depth, and sea surface height (SSH).

The OFGF is defined and applied to the OML in order to propose a dynamical diagnosis of
the maintenance and generating process of the ABFZ. Following GC2014, we use the OFGF as
a tool to unravel the Lagrangian (pure) sources of the oceanic front. While there is
plenty of literature investigating the ocean-front dynamics (e.g., Dinniman and
Rienecker, 1999), the concept of this OFGF has been hardly referred to. The Lagrangian
frontogenesis function, F, is defined as

(1)F≡ddt∂θ∂y,

where θ is the temperature. While
the frontogenetic function is generally defined as the square of the horizontal gradient
of the temperature (e.g., GC2014), our study only employs the meridional gradient of the
temperature because the ABFZ SST-gradient is oriented south–north. The right-hand side
of Eq. (1) can be written as,

Here, u, v, and w denote the zonal, meridional, and vertical current velocities,
respectively. Equation (2) describes the processes that act to generate or destroy the
ocean front. The terms -∂u∂y∂θ∂x, -∂v∂y∂θ∂y, and
-∂w∂y∂θ∂z are the contributions
due to the mechanical processes: shear, convergence, and tilting, respectively. The shear
term represents conversion of the zonal temperature gradient into meridional gradient by
zonal current shear. In particular, the cool SST associated with the Benguela upwelling
creates a strong zonal gradient in the south of the ABFZ (e.g., Morholz et al., 1999).
The shear term can explain the conversion of such a zonal gradient into meridional
gradient. The convergence term represents strengthening or weakening of the meridional
temperature gradient by convergence or divergence of meridional current. The tilting term
represents conversion of the vertical stratification into meridional gradient by
meridional shear of vertical velocity.

The fourth term is a thermodynamical term due to exchange of heat associated with the
turbulent heat flux (surface heat flux is included into w′θ′; it is the surface
boundary condition). The contribution due to the second-order horizontal diffusion is
ignored for simplicity.

Figure 2Climatological seasonal cycle of the temperature (contour) and its
meridional gradient averaged between 10 and 12∘ E for
(a) SST of OISST, (b) SST of CFSR, and (c) OML-mean potential temperature of
CFSR.

Since within the OML the temperature is fairly uniform (cf. Fig. 2 to compare the SST and
OML-averaged temperature), we consider the OFGF with the mixed-layer mean quantities.
With the approximation that temperature is independent of the depth in the OML (e.g.,
Kazmin and Rienecker, 1996; Tozuka and Cronin, 2014), Eq. (2) can be expressed as

where D denotes the OML depth, i.e., the terms with subscript oml include
the changes in the OML implicitly. Although the horizontal velocity is a
function of depth even in the OML, the horizontal mechanical terms in Eq. (3)
can be written in terms of OML-mean quantities because the production is
linear in u and v as long as the temperature is independent of depth in
the OML. Symbols wb, we, Δθ, and D
represent the vertical velocity, the entrainment velocity, the temperature
jump at the bottom of the OML, and the OML depth, respectively. According to
Moisan and Niller (1998), the
entrainment velocity at the bottom of the OML is estimated by

we=∂D∂t+ub⋅∇D,

where ub is the horizontal velocity at the bottom of the OML.
Δθ is estimated as the difference between the OML-mean
temperature and the temperature just below the OML. We use constant values
for sea water density, ρ (1000 kg m−3), and isobaric specific
heat of sea water, Cp (4200 J kg−1 K−1). The
vertical mixing term is replaced with Qs and Qb,
where Qs=-w′θ′‾z=0 is the
surface net heat flux at the top of the OML (downward is positive in this
study) and Qb=-w′θ′‾z=D
represents the vertical mixing at the bottom of the OML, i.e., in the
thermocline. We assume that there is no penetration of shortwave radiation
beyond the OML to deeper ocean layers. Because the vertical turbulent mixing
term at the mixed-layer base Qb is represented according to
K-profile parameterization in ocean–atmosphere general circulation models (OAGCMs), it will not be explicitly
addressed in this study as it is not possible to estimate it from the
reanalysis outputs.

While Eq. (3) is the Lagrangian form of the OFGF, the equation can also be expressed in
Eulerian form as below:

In this equation, the kinematic -∂we∂yΔθD and diabatic Qb entrainment terms, and
the horizontal and vertical advection terms of ∂θoml/∂y, are included in the residual (RESD). Accurate estimation of the entrainment terms are
not possible from CFSR outputs and the horizontal and vertical advection effects are not
related to Lagrangian sources of the frontogenesis. In the remainder of this paper, the
shear term will be referred to as SHER, the confluence as CONF, the tilting as TILT, the
thermodynamic term as SFLX, and the residual as RESD.

Note that our climatology is a 29-year mean from 1982 to 2010 (the procedure of making
daily climatology of temperature meridional gradient and OFGF are described in the
Supplement). However, some years do not have OML data at some grid points around the
coastal region. For these grid points, we make the climatology only for available years.
For example, the smallest number in the focusing ABFZ is 16 years at 16.25∘ S.

Before the dynamical diagnosis is performed, we provide a brief overview of the main
features of the ABFZ. The maximum of the ABFZ (up to 1.4 ∘C per 100 km) is located
at 16∘ S just near the coast (Fig. 1b). Figure 2a shows a seasonal cycle of the
temperature and its meridional gradient obtained from the satellite product OISST. In
this study, the maximum value of the meridional SST gradient is defined as the intensity
of the ABFZ. The core (SST meridional gradient exceeds 1.0 ∘C per 100 km) of the
ABFZ always lies between 17 and 15∘ S. At the climatological seasonal timescale,
the location of the ABFZ exhibits a rather weak variability compared to strong
interannual variability associated with the Benguela Niño events that push the ABFZ
southward due to the southward intrusion of tropical warm water (e.g., Gammelsrød et
al., 1998; Veitch et al., 2006; Rouault et al., 2017). For instance, Rouault et
al. (2017) showed that during the Benguela Niño 2010–2011 the ABFZ displaced
southward as far as 20∘ S. The intensity of the ABFZ shows a pronounced seasonal
cycle: there are two peaks in the strength in April to May and November to December,
respectively. The semiannual cycle of the ABFZ will be examined in more detail in the
following sections. Figure 2b and c evidence that the CFSR reanalysis reproduces
realistically the annual cycle of the ABFZ, and that the annual cycle of the
corresponding OML-mean temperature meridional gradient is representative of the annual
cycle of the SST meridional gradient in terms of both timing and intensity of the two
annual peaks. This latter result justifies our approach to diagnose the frontogenesis of
the ABFZ with the OML-mean quantities.

In this section, we investigate the frontogenesis of the ABFZ by diagnostically applying
the OFGF described in Sect. 3. Figure 3 illustrates the climatological annual-mean
oceanic dynamical fields. The southwestward Angola and northwestward Benguela alongshore
currents collide just south of the ABFZ. Seaward from the ABFZ, a strong westward current
is detected. An intense upwelling (vertical velocity at the bottom of OML exceeding
0.18 m day−1) is generated along the coast in the Benguela
Current region. A local maximum of upwelling in the ABFZ (approximately 17∘ S)
corresponds to one of the most vigorous upwelling cells in the region, namely the Kunene
upwelling cell (Kay et al., 2018). Note also a relatively weak downwelling cell (vertical
velocity down to −0.06 m day−1) just seaward from the Kunene upwelling cell.

5.1 Annual-mean state

Figure 4 presents the annual-mean climatology of the 5 forcing or source terms of the
OFGF superimposing the meridional gradient of the OML-mean temperature. SHER works
frontolytically (destroying the front, about
−2 ∘C per 100 km × 10−7 s−1) in most parts of the ABFZ,
except just near the coast at 17∘ S; although its frontogenetic (generating
front) contribution is rather weak here (less than
2 ∘C per 100 km × 10−7 s−1). CONF has on average an intense
frontogenetic contribution to the ABFZ (up to
5 ∘C per 100 km × 10−7 s−1), especially offshore around
16∘ S, the latitude where the ABFZ is centered (Fig. 2). The frontogenetic
effect of CONF is consistent with GC2014 (the frontogenesis of the SST front associated
with the equatorial Atlantic cold tongue is due to the confluence of the northern South
Equatorial Current and Guinea Current) and can be expected because the warm and cold
currents meet around the ABFZ. Note, however, a small zone just near the coast at
16∘ S where the CONF is frontolytic. This local frontolytic contribution is
overcompensated by a strong frontogenesis due to TILT (more than
5 ∘C per 100 km × 10−7 s−1 on average in the ABFZ core). An
elongated frontogenetic zone associated with TILT is found along the Angolan coast from
17 to 11∘ S and corresponds to the upwelling tongue observed in the Angola
Current region (Fig. 3). On the other hand, TILT is frontolytic off the ABFZ (at
17∘ S, 11∘ E) where the downwelling is dominant as shown in Fig. 3. The
role of the upwelling in the ABFZ development will be analyzed in more detail in
Sect. 6.2.

Figure 3Annual-mean climatological states of OML-mean horizontal current (arrows) and
vertical velocity at the bottom of the OML (color).

In addition to the mechanical terms, the thermodynamical component also shows some
influences on the ABFZ. SFLX works frontogenetically just near the coast at
16∘ S and frontolytically south and north from the core of the ABFZ; although
its contribution is almost negligible compared to the mechanical contribution.
Annual-mean climatology of RESD is estimated from Eq. (4) where the left-hand side (∂θoml/∂y)/∂t is zero for climatology independent of time,

(5)RESD=∂uoml∂y∂θoml∂x+∂voml∂y∂θoml∂y+∂wb∂yΔθD-∂∂yQsρCpD.

Note that all terms in Eq. (5) are for an annual-mean climatology. On average in the
core of the ABFZ, RESD shows a strong frontolytic contribution around the core of the
ABFZ (Fig. 4e). On the other hand, frontogenesis is located in the southern part of the
ABFZ. This may be due to, at least partly, vertical mixing at the base of the OML
accounted for in RESD. In particular, GC2014 showed that for the SST front associated
with the equatorial Atlantic cold tongue, the turbulent mixing (surface and thermocline
heat fluxes) is frontolytic.

Figure 4Annual-mean climatology of each term in OFGF. Contour is annual-mean climatology
of meridional gradient of OML-mean potential temperature of CFSR (∘C per 100 km).
The black box in (a) is the ABFZ used for the analysis in this study.

5.2 Seasonal cycle

In the preceding subsection, we have shown that in terms of climatological
annual-mean, CONF and TILT of the OFGF were the main sources for the ABFZ
generation. Next, we analyze the annual cycle of
the ABFZ and its relationship to the seasonal variations in the OFGF terms.
As shown in Fig. 2, the seasonal cycle of the ABFZ exhibits two peaks. Note
that if the seasonal cycle is sinusoidal, Eq. (4) implies π∕2 phase
shift between the OFGF and temperature meridional gradient. This means that
for a semiannual oscillation the temperature meridional gradient should lag
the OFGF by approximately 1.5 months.

Figure 5a illustrates the box-mean (10–12∘ E and 17–15∘ S) time
series of the meridional gradient of temperature obtained from satellite and reanalysis
products (the time series is smoothed by a 11-day mean moving filter). This box covers
the maximum of the ABFZ in each month since the meridional location of the ABFZ is almost
stable in the climatological seasonal cycle. There is an obvious semiannual cycle of the
ABFZ with maxima in April–May and in November–December, and minima in February–March
and July–August (see also Fig. 2). The first maximum develops rapidly (during 2 months,
from March to April), whereas the development of the second maximum is somewhat slower
(3 months, from August to October). Figure 5a also evidences that CFSR realistically
reproduces the semiannual cycle, although the magnitudes of the CFSR meridional SST
gradient are generally slightly stronger with respect to OISST. Corresponding to the
annual cycle of the ABFZ, there is a seasonal cycle of frontogenesis and frontolysis in
Fig. 5a as the tendency of the ABFZ (green line): two maxima in frontogenesis in
March–April and September–October and in frontolysis in May–June and
December–February. The tendency of the ABFZ is estimated by Eq. (6).

We further analyze the seasonal cycle of the OFGF terms. Similarly to the climatological
state in Fig. 4, the contributions of SHER and SFLX are relatively small and do not seem
to be responsible for either of the two peaks in the ABFZ annual cycle (not shown).
Figure 5b shows the seasonal variations of TILT, CONF, and RESD averaged over the same
box as the temperature gradients in Fig. 5a. For estimation of seasonal variation in
RESD, the tendency of the meridional gradient is calculated as

(6)∂∂t∂θoml(t)∂y=∂θoml(t+Δt)∂y-∂θoml(t-Δt)∂y2Δt,

where t and Δt denote each time step and difference in time step; in this
case, Δt is 1 day (86 400 s). With this tendency at each day, RESD(t) is
estimated by

RESD(t)=∂∂t∂θoml(t)∂y-SHER(t)-CONF(t)-TILT(t)-SFLX(t).

From the middle of November to February, the box-averaged CONF is modestly negative,
which is due to the frontolytic effect adjacent to the Angolan coast as shown in Fig. 4b
(however, CONF is frontogenetic off the ABFZ). The contribution of CONF becomes positive
from March, although its frontogenetic contribution is relatively weak
(< 1.0 ∘C per 100 km × 10−7 s−1) until July. From the
end of July CONF starts to increase and reaches its maximum
(3.0 ∘C per 100 km × 10−7 s−1) at the end of August. The
frontogenetic contribution of CONF remains strong until the beginning of October but then
rapidly decrease to become frontolytic in November.

The contribution of TILT to the ABFZ seasonal cycle is almost always frontogenetic. Close
to zero in January, TILT is enhanced from February and reaches its maximum value
(3.0 ∘C per 100 km × 10−7 s−1) in March–April. In May–June,
the frontogenetic effect of TILT gradually decreases (down to
1.0 ∘C per 100 km × 10−7 s−1) until December. The maxima in
TILT and CONF correspond to the two periods of development of the ABFZ at the seasonal
timescale: from March to April and from August to October, respectively (Fig. 5a). This
suggests that the two peaks of the ABFZ are associated with two different mechanical
terms and thus are due to two different physical processes. On the other hand, the two
periods of decay of the ABFZ are consistent with the periods of weak frontogenetic and/or
frontolytic contributions of both TILT and CONF (as observed by Mohrholz et al., 1999) in
December–February and June–July, respectively.

In addition, RESD is almost always frontolytic with a relatively large oscillation (0.0
to −5.0 ∘C per 100 km × 10−7 s−1) as shown in Fig. 5b. In
particular, the frontolytic effect due to RESD is stably strong (around
−3.0 ∘C per 100 km × 10−7 s−1) from May–August when the ABFZ
becomes weakened and frontogenetic effects due to CONF and TILT are relatively weak
(Fig. 5a and b). In contrast with TILT and CONF, RESD does not exhibit a clear signal of
semiannual cycle, but rather an annual cycle. We thus can conclude that in terms of a
first-order estimation, the semiannual cycle of the ABFZ is explained by the combination
of TILT and CONF.

The previous section showed that the two periods of development of the ABFZ in
March–April and August–October were due, to a large extent, to the contribution of TILT
and CONF, respectively. In this section, we investigate what components are responsible
for the corresponding peaks in TILT and CONF.

6.1 Meridional confluence

CONF represents changes in the meridional temperature gradient associated with ocean
dynamics of convergence or divergence of meridional current, ∂voml/∂y. Figure 6a presents the annual cycle of ∂voml/∂y averaged over the ABFZ. In the ABFZ, the meridional current is almost always
convergent except for weak divergence from November to January. The convergence of the
meridional current is maximum from August to mid-October (up to
−3.0 × 10−7 s−1) and is rapidly weakened during November. The
seasonal fluctuations in the convergence are associated with changes in intensity and
meridional extension of the southward Angola Current and northward Benguela Current that
meet in the ABFZ. Around the ABFZ, an area of lower SSH is formed, associated with the
Angola Dome (the cold dome identified by Mazeika, 1967), which shows a pronounced
seasonal cycle (e.g., Doi et al., 2007). Such well-organized SSH spatial variability
induces the geostrophic current, which can contribute to the current system around the
ABFZ. Therefore, here we also focus on the SSH and corresponding geostrophic current.
Figure 6b illustrates the annual cycle of the OML-mean meridional current and meridional
component of geostrophic current estimated from SSH at 15∘ S (north of the core
of the ABFZ) and 17∘ S (south of the core of the ABFZ) averaged between 10 and
12∘ E. At 15∘ S the OML-mean meridional current is southward all year
round, except for the beginning of May when a weak northward flow is observed. The
maximum southward meridional velocity occurs in October (−0.12 m s−1). At
17∘ S the OML-mean meridional current is northward in March–June and shows a
biannual peak of southward current in January to mid-February and October indicating
intrusion of tropical warm water to the ABFZ (e.g., Rouault, 2012). Figure 6b clearly
evidences that the region between 17 and 15∘ S is expected to be convergent. The
most convergent period is in September–October when the CONF contribution to
frontogenesis is the largest as shown in Fig. 5b. Another relatively strong convergent
period is from April to June when the meridional current is rather northward at
17∘ S and close to zero at 15∘ S. The period of weak convergence or
divergence, from December to February, corresponds to frontolytic contribution of CONF
(Fig. 5b). Figure 6b evidences that the OML-mean meridional current can be explained, to
a large extent, by the geostrophic surface current. While a large part of the meridional
current and its seasonal cycle around the ABFZ is explained by geostrophic current
associated with the SSH to the northwest of the ABFZ, there are some differences between
voml and vg. These differences are due to the Ekman and
ageostrophic currents.

Figure 6Time series of (a) averaged over (17–15∘ S and
10–12∘ E) and (b) OML-mean meridional current velocity (black) and
geostrophic meridional current velocity estimated from sea surface height (blue) at
15∘ S (solid line) and 17∘ S (+ mark) averaged between 10 and
12∘ E. All variables are filtered by a moving 11-day window.

The spatial distributions of the climatological monthly-mean SSH and surface geostrophic
current in January, April, and September are shown in Fig. 7. Two local minima of SSH are
observed: one along the coast in the Benguela system and one west of the ABFZ (centered
at 14∘ S and 6∘ E). The latter is associated with the Angola Dome
(e.g., Doi et al., 2007) and a strong cyclonic geostrophic flow reaching the ABFZ. The
geostrophic current generally generates the convergence in the ABFZ (Fig. 6a). However,
in January an intense divergence is generated due to the strong southward ageostrophic
current along the coast (Fig. 7a). In April, when CONF is modestly frontogenetic
(Fig. 5b), the Angola Dome and associated geostrophic flow are diminished (Fig. 7b) and a
main source of convergence can thus be attributed to the northward Benguela Current that
penetrates into the ABFZ as far as 16∘ S. In September, although the low SSH
sits in the south of the ABFZ as in April, the Angola Dome is significantly developed to
be related to a strong geostrophic current resulting in a strong southward Angola Current
intruding into the ABFZ along the Angolan coast. The northward Benguela Current is
relatively weak in September compared to that in April. Thus, the maximum CONF in
September is due to the strong southward Angola Current.

6.2 Tilting

TILT is the second main contributor to generate the ABFZ especially in March to May as
shown in Figs. 4 and 5. In a first approximation, TILT results from the meridional
gradient of vertical motion ∂wb/∂y convoluted with the
thermocline stratification (e.g., Eq. 4). Here, we explore more details of upwelling in
the ABFZ. The annual cycle of these two components averaged over the box
12–10∘ E and 17–15∘ S (Fig. 8) points out the negative ∂wb/∂y and the positive stratification from January to August,
respectively. This configuration leads to frontogenesis through the TILT term (Fig. 5b).
From August to December, ∂wb/∂y changes sign and the
stratification becomes weaker; that explains why the TILT term is frontolytic (especially
in September) and its magnitude is weaker compared to January–August because of a weaker
stratification (smaller vertical gradient in temperature). Negative ∂wb/∂y can be seen in both March–April and August–September around
the ABFZ in Fig. S1a and b in the Supplement, but positive ∂wb/∂y are also generated around the ABFZ more in August–September than in
March–April.

Figure 8Time series of the area-averaged meridional gradient of the vertical
velocity at the bottom of OML (black), OML depth (blue), intensity of
upper-ocean thermocline stratification (red) over 17–15∘ S and
10–12∘ E. All variables are filtered by a moving 11-day window.

The OML depth has extrema in August–September (around 100 m) and from January–April
(around 20 m) indicating the seasonal cycle of solar insolation forcing and wind-driven
mixing. Also, the intensity of the thermocline shows a strong stratification from March
to May (2 ∘C) and weak stratification from September to November
(1.2 ∘C). From March to May TILT is the most dominant frontogenetic source
because the OML is the shallowest (20–30 m), the stratification is the strongest
(temperature jump in the thermocline up to 2.0 K), and the shear of vertical velocity
∂wb/∂y is strongly negative. The shallow OML and strong
stratification can amplify the tilting effect due to ∂wb/∂y.
Conversely, TILT is weakly frontolytic from August to September when the OML depth is
deepened (∼100 m), the stratification is weak (1.2 K), and ∂wb/∂y is positive. Figure S1c and d shows the differences in OML depth and ocean
stratification between March–April and August–September. Shallower OML and stronger
stratification can be seen everywhere around the ABFZ. Therefore, effects of both
positive and negative ∂wb/∂y are reduced and consequently,
the contribution of TILT is quite weak in August–September (Fig. 5b).

In this study we investigated the processes controlling the ABFZ evolution based on a
first-order estimation of an ocean frontogenetic function (OFGF) applied to the ocean
mixing layer (OML) derived from the CFSR reanalysis. The OFGF represents the temporal
evolution of the meridional mixed-layer temperature gradient and contains three
mechanical terms (shear, convergence and tilting) and one thermodynamical term. The
residual term accounts for, in particular, vertical mixing at the bottom of the OML
(which is based on parameterization of turbulence, i.e., highly nonlinear processes),
entrainment velocity, and horizontal or vertical advection of the meridional temperature
gradient. An analysis of the annual mean OFGF suggests that the confluence effect (CONF)
due to southward Angola Current (warm) and northward Benguela Current (cold) is
dominantly frontogenetic over the offshore part of the ABFZ, although it has a local
frontolytic effect just near the coast at 16∘ S. The tilting effect (TILT)
related to the coastal upwelling regime is another main contributor to frontogenesis.
Around the ABFZ, intense Ekman transport divergence is generated by wind stress curl
(Fig. S2). This Ekman divergence induces upward motion in the Ekman layer. Interestingly,
the Ekman divergence due to the zonal wind stress is also an important contributor to the
vertical velocity in the ABFZ. The contributions of the shear (SHER) and surface heat
flux (SFLX) terms are rather negligible, while the residual (RESD) term represents a main
frontolytic source.

Climatological seasonal evolution of the ABFZ has a well-pronounced semiannual cycle with
two maxima of the SST meridional gradient, in April–May and November–December, and two
minima, in February–March and July–August. We showed that the two maxima of the ABFZ
were associated with two different mechanical terms and due to two different physical
processes. The development of the first ABFZ maximum during March–April is mainly
explained by the strong contribution of TILT to frontogenesis, while the development of
the second ABFZ maximum during September–October is due to the frontogenetic
contribution of CONF. TILT is associated with the meridional gradient of the vertical
velocity. The annual maximum of TILT in March–April is due, to a large extent, to the
combination of the maximum stratification (Δθ), shallow OML depth (D),
and negative ∂wb/∂y during this period. Indeed, in OFGF the
ratio ΔθD represents the efficiency by which the meridional
gradient of the coastal upwelling velocity can lead to the change of the ABFZ intensity.
Although the OML depth also modulates the surface heat flux contribution to the OFGF, the
thermodynamical term does not show any significant impact on the development of the ABFZ
maximum in March–April. On the other hand, the importance of the OML depth for the
thermodynamical term was suggested for frontogenesis in a SST front associated with
western boundary current (Tozuka and Cronin, 2014; Tozuka et al., 2018). The annual
maximum of CONF in September–October is related to an intensified southward Angola
Current that seems to be induced by an approximately cyclonic geostrophic flow associated
with the development of the Angola Dome (e.g., Doi et al., 2007). However, the
geostrophic current is not completely consistent with the OML-mean current. The
difference can be attributed to the Ekman transport and ageostrophic component. A
relatively smaller contribution of CONF to frontogenesis is also observed in April and is
due to the intrusion of the northward Benguela Current to the ABFZ during this period.

Most CGCMs fail to reproduce realistic SST fields and ABFZ locations with
respect to climatology. Among other causes, this can be due to a poor
representation of regional climate variables in CGCMs (such as
upwelling-favorable wind, wind drop off, and consequently near-coastal wind
curl, alongshore stratification, and OML depth (e.g., Xu et al., 2014; Koseki
et al., 2018; Goubanova et al., 2018), which directly impact the two main
frontogenesis terms (CONF and TILT). The OFGF proposed in the present study
can thus be an appropriate tool to diagnose the performance of CGCMs in the
ABFZ and more generally in frontal zones. This study shows that diagnoses
developed for mesoscale studies are valuable for climate studies and can help
to identify the origin of biases that affect ocean general circulation models (OGCMs).

Although the present study focused on the climatological state of the ABFZ and its
seasonal cycle, the intensity and the location of the ABFZ exhibits a strong interannual
variability (e.g., Mohrholz et al., 1999; Rouault et al., 2017). Further investigation on
how the contributions of the OFGF are modified in the case of the Benguela
Niño/Niña would provide further insight into the dynamics of the southeastern
tropical Atlantic and sources of the CGCMs bias that have been suggested to develop as
interannual warm events (e.g., Xu et al., 2014).

Effects of the turbulent mixing and the effect due to the entrainment velocity at the
mixed-layer base on frontogenesis were accounted for by the residual of the frontogenetic
function. An accurate quantification of these effects requires using simulations of a
higher resolution ocean model for which the output of the temperature tendency due to
those processes are available. According to Giordani and Caniaux (2014), the vertical
mixing is also a large contributor to the frontogenesis. However, by destroying the
balance between the mass and circulation fields, the assimilation procedure induces
spurious effects on the entrainment processes, which justifies that this process was
included in the residual term RESD. These are the main limitations of this study because
diapycnal mixing is often an important term of the oceanic upper-layers heat budget,
which is tightly coupled with vertical motions (Giordani et al., 2013). A more
comprehensive understanding of this term would be valuable to estimate the performance of
CGCMs in the ABFZ and more generally in coastal upwelling zones.

SK derived the ocean frontogenetic function (OFGF) by discussing with HG and
KG and improved the OFGF. SK performed the main analysis of the data and all
authors contributed to the interpretation of the results and discussion. SK
wrote a first draft and HG and KG improved the draft extensively with
constructive and critical comments on the draft.

We greatly appreciate two anonymous reviewers for their constructive and
helpful comments. Also, we would like to express our appreciation to
Kunihiro Aoki in the University of Tokyo for his constructive discussion in
the initial stage of this study. We also thank Guy Caniaux in
Météo-France for their helpful discussions. We used the 2012Rb
versions of the MATLAB software package provided by MathWorks, Inc.,
(http://www.mathworks.com, last access: 13 August 2018) and Grid
Analysis and Display System (GrADS, http://cola.gmu.edu/grads/, last
access: 30 November 2018) to compute each dataset and create figures.
Shunya Koseki has received funding from the EU FP7/2007–2013 under grant
agreement no. 603521 (EU-PREFACE) and STERCP (ERC, grant no. 648982).
Katerina Goubanova was also supported by FONDECYT (grant 1171861).

Goubanova, K., Sanchez, G., E., Frauen, C., and Voldoire A.: Role of remote
and local wind stress forcing in the development of the warm SST errors in
the southeastern tropical Atlantic in a coupled high-resolution model, Clim.
Dynam., 2018.

With an ocean frontogenetic function, the frontogenesis of the Angola–Benguela Frontal Zone (ABFZ) is investigated. On an annual-mean timescale, the meridional confluence of Angola and Benguela currents and tilting effect due to the upwelling are the main sources to generate the ABFZ. The annual cycle of the ABFZ is also mainly driven by these two effects.

With an ocean frontogenetic function, the frontogenesis of the Angola–Benguela Frontal Zone...